Revised QRF Habitat Capacity Model and RF Extrapolation Model Brief

¹ Mount Hood Environmental, PO Box 1303, Challis, Idaho, 83226, USA
² Mount Hood Environmental, 39085 Pioneer Boulevard #100 Mezzanine, Sandy, Oregon, 97055, USA
³ Mount Hood Environmental, PO Box 4282, McCall, Idaho, 83638, USA

^✉ Correspondence: Bryce N. Oldemeyer <bryce.oldemeyer@mounthoodenvironmental.com>, Mark Roes <mark.roes@mthoodenvironmental.com>

1 Background

Quantile random forest (QRF) models have become popular for quantifying freshwater habitat carrying capacity due to their flexible framework that avoids common pitfalls associated with noisy data, correlated variables, and non-linear relationships. Recently, three QRF models were fit with fish-habitat data from fish observation studies and the Columbia Habitat Monitoring Program (CHaMP) and used to estimate habitat carrying capacity for ESA-listed populations of Chinook salmon and steelhead during three critical life-stages (juvenile summer parr, juvenile winter presmolt, and adult redds) for wadable streams within the Columbia River Basin. Model covariates were selected from >100 habitat metrics and chosen for their high predictive power (Appendix B of Idaho OSC Team, 2019; See et al. 2021). Since then, additional emphasis has been placed on the utility of the QRF capacity models to inform restoration project design and monitoring and increase the spatial extent of fish-habitat data using streamlined protocols (DASH - Carmichael et al. 2019). Therefore, we conducted a revised covariate selection process for the QRF models that prioritized 1) predictive power, 2) compatability with future DASH data collection, 3) informing restoration project development and monitoring, 4) minimal imputation for missing CHaMP data, and 5) low covariate correlation. Additionally, we evaluated the assumption made during initial QRF model development that a single model was appropriate for both Chinook salmon and steelhead during each of the three life stages.

Similarly, a random forest (RF) extrapolation model was used to predict habitat capacity across larger spatial scales where CHaMP and/or DASH data weren’t available (Appendix B of Idaho OSC Team). We revisited the globally available attributes (GAAs) included in the original RF extrapolation model and made minor modifications to the model that maintained covariates with high predictive power and included metrics that better aligned with the revised QRF model. To evaluate the differences between the original and revised QRF/RF models, we compared watershed carrying capacity estimates produced by the both sets of models for eight watersheds located within the Upper Salmon River basin.

This process resulted in revised QRF and RF extrapolation models that were more informative for restoration design and monitoring, included covariates that could be calculated using newly developed stream habitat protocols, and maintained a similar level of predictive power as the original models.

2 Revised QRF Habitat Capacity Model

2.1 Covariate selection process

Habitat covariates for the QRF habitat capacity models were generated from the CHaMP dataset or obtained from other publicly available sources (e.g. NorWest stream temperature data). In total, 129 habitat metrics were examined in the selection process. Covariates were aggregated into eleven metric categories and 1-4 covariates were chosen from each category based on following criteria:

1. What was the strength between the covariate and the response variable (based on MIC score)?

2. Could the covariate be calculated using DASH data?

3. Was the covariate informative for restoration efforts?

4. How much data were missing and/or the amount of “0”s for the covariate in the fish-habitat dataset?

5. How correlated was the covariate with other covariates within the same metric category, particularly covariates with higher MIC scores?

Below is a simplified, theoretical example of how a covariate might be selected for a model.

–

In the original QRF model, discharge was included as a covariate because it had a high MIC score and it made biological sense (i.e. discharge is a significant factor impacting fish habitat use and, presumably, habitat carrying capacity). Unfortunately, discharge isn’t that informative for restoration efforts because most restoration actions can’t create water. Discharge, like many habitat metrics, is highly correlated with other potential covariates which may have been left out of the original QRF model for any number of reasons (highly correlated with other model covariates, excluded to avoid overfitting, etc.). Using the revised model selection criteria, we observed that average thalweg depth has a MIC score nearly as high as discharge, is informative for restoration efforts, can be calculated from DASH, and is highly highly correlated with discharge. Based on all the information above, mean thalweg depth would be substituted for discharge in the model.

–

The covariate selection process was conducted independently for both species for all three life stages to test the assumption made during the original QRF model development that it was appropriate to apply the same life stage models to both species.

2.2 Covariate selection results

There were 12-14 covariates selected for each of the six QRF habitat capacity models. While the relative importance of the final covariates in the three life stage models differed between species, the final covariates themselves were nearly identical. (Figure 2.1 , Figure 2.2, and Figure 2.3 ). This confirmed that one model for both species per life stage was appropriate. Therefore, we consolidated the species-specific models into a single winter juvenile, summer juvenile, and redd models. (Table 2.1). Examination of covariate partial dependence plots from the revised QRF habitat capacity models indicated effects that were generally biologically intuitive and can be found in Section @ref(revised-qrf-habitat-capacity-model—partial-dependence-plots)

Figure 2.1: Relative importance plots for covariates included in the revised juvenile summer QRF models

Figure 2.2: Relative importance plots for covariates included in the revised juvenile winter QRF models

Figure 2.3: Relative importance plots for covariates included in the revised QRF redds models

Table 2.1: Habitat covariates and their descriptions for three revised life stage QRF capacity models. Numbers indicate where each metric ranked in relative importance for each species. Dashes indicate the metric was not used for a given model.

Name	Metric Category	Juv Sum Chnk	Juv Sum Sthd	Juv Win Chnk	Juv Win Sthd	Redds Chnk	Redds Sthd	Description
Channel Unit Frequency	ChannelUnit	5	9	6	3	1	1	Number of channel units per 100 meters.
Fast NonTurbulent Frequency	ChannelUnit	6	13	–	–	13	4	Number of Fast Water Non-Turbulent channel units per 100 meters.
Sinuosity	Complexity	13	7	11	10	10	12	Ratio of the thalweg length to the straight line distance between the start and end points of the thalweg.
Wetted Channel Braidedness	Complexity	14	14	13	13	–	–	Ratio of the total length of the wetted mainstem channel plus side channels and the length of the mainstem channel.
Fish Cover: LW	Cover	–	–	4	9	–	–	Percent of wetted area that has woody debris as fish cover.
Fish Cover: Some Cover	Cover	8	4	9	8	9	3	Percent of wetted area with some form of fish cover
Residual Depth	Size	–	–	2	2	–	–	Average residual depth of the channel unit.
Average Thalweg Depth	Size	1	3	–	–	2	2	Average Thalweg Depth, meters
Thalweg Exit Depth Avg	Size	–	–	7	6	–	–	Depth of the thalweg at the downstream edge of the channel unit.
Gradient	Size	3	2	5	1	4	6	Site water surface gradient is calculated as the difference between the top of site (upstream) and bottom of site (downstream) water surface elevations divided by thalweg length.
Residual Pool Depth	Size	12	10	–	–	11	5	The average difference between the maximum depth and downstream end depth of all Slow Water/Pool channel units.
Discharge	Size	–	–	3	4	–	–	The sum of station discharge across all stations. Station discharge is calculated as depth x velocity x station increment for all stations except first and last. Station discharge for first and last station is 0.5 x station width x depth x velocity.
Substrate Est: Boulders	Substrate	10	12	–	–	8	11	Percent of boulders (256-4000 mm) within the wetted site area.
Substrate Est: Cobble and Boulder	Substrate	–	–	10	11	–	–	Total cobble plus boulder percentage
Substrate Est: Cobbles	Substrate	11	6	–	–	5	8	Percent of cobbles (64-256 mm) within the wetted site area.
Substrate Est: Coarse and Fine Gravel	Substrate	7	8	12	12	7	13	Percent of coarse and fine gravel (2-64 mm) within the wetted site area.
Substrate Est: Sand and Fines	Substrate	9	5	8	7	6	7	Percent of sand and fine sediment (0.01-2 mm) within the wetted site area.
Avg. August Temperature	Temperature	2	1	–	–	3	10	Average predicted daily August temperature from NorWest, averaged across the years 2002-2011.
Elevation	Temperature	–	–	1	5	–	–	Elevation, meters
Large Wood Frequency: Wetted	Wood	4	11	–	–	12	9	Number of large wood pieces per 100 meters within the wetted channel.

3 Revised RF Extrapolation Model

The spatial extent of QRF capacity predictions is limited to reaches with high-resolution habitat data (i.e. CHaMP or DASH data). To estimate capacity outside of the QRF habitat capacity spatial extent, an extrapolation model fit to “globally available attributes” (GAAs) obtained from a continuous, linear stream network created by Morgan Bond and Tyler Nodine (https://www.fisheries.noaa.gov/resource/data/columbia-basin-historical-ecology-project-data) was used for the entire Columbia River Basin. A random forest model was fit using the GAAs from the linear stream network and used to estimate habitat capacity for the entire Columbia River Basin at a 200 meter reach scale. Consistent with the QRF habitat capacity models, the RF extrapolation model makes no assumptions about the direction and distribution of effects of predictors, and constrains capacity estimates within the range of predictions produced by the QRF habitat capacity model. However, random forest methods do not account for variable strata weights across the CHaMP dataset, a source of potential bias that could be alleviated through the collection of additional paired fish and habitat data.

RF extrapolation model covariates were selected from the list of GAAs and evaluated for inclusion by examining relative importance plots (Figure 3.1, Figure 3.2, and Figure 3.3 ), partial dependence plots (Section @ref(revised-rf-extrapolation-model—partial-dependence-plots)) , and correlations between covariates. We used the previous extrapolation model as a starting point for covariate selection. This resulted in the replacement of the “regime” covariate (a categorical indicator of dominant precipitation type) for elevation and the removal of relative slope, which we found was redundant with gradient. Model results indicated that elevation was consistently one of the most important predictors in the model. This is particularly evident in the Chinook parr summer model where capacity predictions were primarily driven by elevation.

Figure 3.1: Relative importance plots for covariates included in the revised juvenile summer RF extrapolation models

Figure 3.2: Relative importance plots for covariates included in the revised juvenile winter RF extrapolation models

Figure 3.3: Relative importance plots for covariates included in the revised juvenile winter RF extrapolation models

Table 3.1: Globally available attritibutes (GAAs) and their descriptions used in the random forest extrapolation model.

Metric	Decription
Gradient %	Stream gradient (%).
Sinuosity	Reach sinuosity. 1 = straight, 1 < sinuous.
Alpine accumulation	Number of upstream cells in alpine terrain.
Fines accumulation	Number of upstream cells in fine grain lithologies.
Flow accumulation	Number of upstream DEM cells flowing into reach.
Gravel accumulation	Number of upstream cells in gravel producing lithologies.
Precipitation accumulation	Number of upstream cells weighted by average annual precipitation.
Floodplain width	Current unmodified floodplain width.
Avg Aug stream temperature	Historical composite scenario representing 10 year average August mean stream temperatures for 2002-2011 (Isaak et al. 2017).
Disturbance PCA 1	Disturbance Classification PCA 1 Score (Whittier et al. 2011).
Natural PCA 1	Natural Classification PCA 1 Score (Whittier et al. 2011).
Natural PCA 2	Natural Classification PCA 2 Score (Whittier et al. 2011).
Elevation	Elevation at downstream end of reach

3.1 Habitat capacity estimates

Habitat carrying capacity was estimated with the revised QRF and RF extrapolation models for Chinook salmon and steelhead during juvenile summer, juvenile winter, and redd life stages for eight watersheds in the Upper Salmon River Basin. Spatial domains for species were originally defined by Streamnet (https://www.streamnet.org/home/data-maps/gis-data-sets/) and revised based on expert knowledge from regional biologists.

3.1.1 Chinook

Figure 3.4: Extrapolations of habitat capacity for Chinook salmon, by life-stage, for the eight watersheds within the Upper Salmon River Basin using the revised models.

Table 3.2: Predicted Chinook salmon habitat capacity by life-stage and watershed using the revised models.

Watershed	Juv summer capacity	Summer SE	Juv winter capacity	Winter SE	Redd capacity	Redd SE
EF Salmon	1,926,623	226,925.7	138,214	32,880.3	402	20.7
Lemhi	786,452	62,659.8	141,515	15,358.7	353	11.0
NF Salmon	339,275	50,147.9	70,462	10,409.3	166	7.8
Pahsimeroi	265,099	18,409.2	86,999	9,780.7	139	4.4
Panther Cr	1,219,542	118,369.5	201,265	22,296.2	448	16.5
Upper Salmon	3,301,286	352,419.5	166,522	45,582.4	575	28.6
Valley Cr	1,902,198	207,362.9	115,517	32,535.0	394	19.7
Yankee Fork	2,144,056	274,555.8	119,298	28,782.6	438	23.0

Table 3.2: Predicted Chinook salmon habitat capacity per kilometer by life-stage and watershed using the revised models.

Watershed	Juv summer capacity/km	Summer SE/km	Juv winter capacity/km	Winter SE/km	Redd capacity/km	Redd SE/km
EF Salmon	12,335	1,452.9	885	210.5	3	0.1
Lemhi	5,766	459.4	1,038	112.6	3	0.1
NF Salmon	6,504	961.3	1,351	199.5	3	0.1
Pahsimeroi	5,146	357.3	1,689	189.8	3	0.1
Panther Cr	8,544	829.3	1,410	156.2	3	0.1
Upper Salmon	17,082	1,823.5	862	235.9	3	0.1
Valley Cr	15,833	1,726.0	961	270.8	3	0.2
Yankee Fork	14,967	1,916.6	833	200.9	3	0.2

3.1.2 Steelhead

Figure 3.5: Extrapolations of habitat capacity for steelhead, by life-stage, for the eight watersheds within the Upper Salmon River Basin using the revised models.

Table 3.3: Predicted steelhead habitat capacity by life-stage and watershed using the revised models.

Watershed	Juv summer capacity	Summer SE	Juv winter capacity	Winter SE	Redd capacity	Redd SE
EF Salmon	252,597	15,520.5	337,682	36,795	413	24
Lemhi	310,577	9,082.3	363,898	27,441	441	18
NF Salmon	242,471	18,381.8	313,118	27,955	323	22
Pahsimeroi	159,705	6,225.1	205,921	13,951	198	8
Panther Cr	268,476	13,598.0	339,671	19,946	317	15
Upper Salmon	243,548	14,843.6	310,879	39,013	452	32
Valley Cr	176,048	10,707.6	288,579	31,329	365	26
Yankee Fork	197,926	12,378.9	341,310	38,555	449	36

Table 3.3: Predicted steelhead habitat capacity per kilometer by life-stage and watershed using the revised models.

Watershed	Juv summer capacity/km	Summer SE/km	Juv winter capacity/km	Winter SE/km	Redd capacity/km	Redd SE/km
EF Salmon	1,525	93.7	2,039	222.2	2	0.1
Lemhi	1,774	51.9	2,079	156.8	3	0.1
NF Salmon	2,049	155.3	2,646	236.2	3	0.2
Pahsimeroi	1,924	75.0	2,481	168.1	2	0.1
Panther Cr	2,105	106.6	2,664	156.4	2	0.1
Upper Salmon	1,485	90.5	1,895	237.8	3	0.2
Valley Cr	1,465	89.1	2,401	260.7	3	0.2
Yankee Fork	1,249	78.1	2,154	243.4	3	0.2

3.2 Habitat capacity estimates compared with previous QRF and extrapolation

Comparisons of watershed capacity estimates between the previous and revised QRF and RF extrapolation models reveal modest differences in most cases, with the exception of Chinook parr summer capacities in several watersheds. The substantial increases observed for Chinook parr summer capacity were likely due to the inclusion of the elevation coviariate in the RF extrapolation model, and increases range from 13 - 222% compared to the previous extrapolation.

3.2.1 Chinook

Figure 3.6: Change in predicted Chinook salmon habitat capacity estimates from the original model and extrapolation, by life-stage, for the eight watersheds within the Upper Salmon River Basin.

Table 3.4: Estimated Chinook salmon capacities and comparison with previous random forest extrapolations for eight watersheds

Model	Watershed	Capacity per km	Total capacity	Capacity % change	Capacity SE
Juv summer	EF Salmon	12,335.5	1,926,623	112	226,926
Juv summer	Lemhi	5,765.9	786,452	112	62,660
Juv summer	NF Salmon	6,503.6	339,275	13	50,148
Juv summer	Pahsimeroi	5,145.6	265,099	45	18,409
Juv summer	Panther Cr	8,543.7	1,219,542	21	118,369
Juv summer	Upper Salmon	17,081.6	3,301,286	163	352,419
Juv summer	Valley Cr	15,832.8	1,902,198	152	207,363
Juv summer	Yankee Fork	14,967.3	2,144,056	222	274,556
Juv winter	EF Salmon	884.9	138,214	0	32,880
Juv winter	Lemhi	1,037.5	141,515	-8	15,359
Juv winter	NF Salmon	1,350.7	70,462	28	10,409
Juv winter	Pahsimeroi	1,688.7	86,999	-8	9,781
Juv winter	Panther Cr	1,410.0	201,265	29	22,296
Juv winter	Upper Salmon	861.6	166,522	-29	45,582
Juv winter	Valley Cr	961.5	115,517	-12	32,535
Juv winter	Yankee Fork	832.8	119,298	20	28,783
Redds	EF Salmon	2.6	402	-13	21
Redds	Lemhi	2.6	353	5	11
Redds	NF Salmon	3.2	166	-5	8
Redds	Pahsimeroi	2.7	139	25	4
Redds	Panther Cr	3.1	448	-4	17
Redds	Upper Salmon	3.0	575	-20	29
Redds	Valley Cr	3.3	394	-29	20
Redds	Yankee Fork	3.1	438	-38	23

3.2.2 Steelhead

Figure 3.7: Change in steelhead habitat capacity estimates from the original model and extrapolation, by life-stage, for the eight watersheds within the Upper Salmon River Basin.

Table 3.5: Estimated steelhead capacities and comparison with previous random forest extrapolations for eight watersheds

Model	Watershed	Capacity per km	Total capacity	Capacity % change	Capacity SE
Juv summer	EF Salmon	1,525.4	252,597	-31	15,521
Juv summer	Lemhi	1,774.2	310,577	-15	9,082
Juv summer	NF Salmon	2,048.7	242,471	-5	18,382
Juv summer	Pahsimeroi	1,924.2	159,705	-18	6,225
Juv summer	Panther Cr	2,105.3	268,476	-8	13,598
Juv summer	Upper Salmon	1,484.6	243,548	-31	14,844
Juv summer	Valley Cr	1,465.0	176,048	-28	10,708
Juv summer	Yankee Fork	1,249.4	197,926	-29	12,379
Juv winter	EF Salmon	2,039.2	337,682	-14	36,795
Juv winter	Lemhi	2,078.7	363,898	-8	27,441
Juv winter	NF Salmon	2,645.6	313,118	-1	27,955
Juv winter	Pahsimeroi	2,481.0	205,921	-4	13,951
Juv winter	Panther Cr	2,663.6	339,671	8	19,946
Juv winter	Upper Salmon	1,895.1	310,879	-26	39,013
Juv winter	Valley Cr	2,401.4	288,579	-14	31,329
Juv winter	Yankee Fork	2,154.4	341,310	-18	38,555
Redds	EF Salmon	2.5	413	-13	24
Redds	Lemhi	2.5	441	10	18
Redds	NF Salmon	2.7	323	-10	22
Redds	Pahsimeroi	2.4	198	2	8
Redds	Panther Cr	2.5	317	-7	15
Redds	Upper Salmon	2.8	452	-11	32
Redds	Valley Cr	3.0	365	-20	26
Redds	Yankee Fork	2.8	449	-25	36

4 Supplemental Figures and Tables

4.1 Partial dependence plots

To support the covariate selection process for the QRF capacity and RF extrapolation models, we generated partial dependence plots that illustrate the predicted effect of covariates on fish density and capacity. These function similarly to traditional covariate effects plots where predictions on the response are made by altering the value of the covariate of interest while all others are fixed at mean values. Because random forest models do not place any constraints on the possible mathematical relationships between predictor and response variables, effects curves have been visualized using smoothing methods (LOESS) and may not reflect actual model behavior across the range of covariate values.

4.1.1 Revised QRF habitat capacity model

Figure 4.1: Partial dependence plots for covariates included in the revised juvenile summer QRF models

Figure 4.2: Partial dependence plots for covariates included in the revised juvenile summer QRF models

Figure 4.3: Partial dependence plots for covariates included in the revised juvenile winter QRF models

Figure 4.4: Partial dependence plots for covariates included in the revised juvenile winter QRF models

Figure 4.5: Partial dependence plots for covariates included in the revised QRF redds models

Figure 4.6: Partial dependence plots for covariates included in the revised QRF redds models

4.1.2 Revised RF extrapolation model

Figure 4.7: Partial dependence plots for covariates included in the revised juvenile summer RF extrapolation models

Figure 4.8: Partial dependence plots for covariates included in the revised juvenile summer RF extrapolation models

Figure 4.9: Partial dependence plots for covariates included in the revised juvenile summer RF extrapolation models

Figure 4.10: Partial dependence plots for covariates included in the revised juvenile summer RF extrapolation models

Figure 4.11: Partial dependence plots for covariates included in the revised juvenile winter RF extrapolation models

Figure 4.12: Partial dependence plots for covariates included in the revised juvenile winter RF extrapolation models

Figure 4.13: Partial dependence plots for covariates included in the revised juvenile winter RF extrapolation models

Figure 4.14: Partial dependence plots for covariates included in the revised juvenile winter RF extrapolation models

Figure 4.15: Partial dependence plots for covariates included in the revised redds RF extrapolation models

Figure 4.16: Partial dependence plots for covariates included in the revised redds RF extrapolation models

Figure 4.17: Partial dependence plots for covariates included in the revised redds RF extrapolation models

Figure 4.18: Partial dependence plots for covariates included in the revised redds RF extrapolation models